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Generating functions defined in terms of algebraic operations on real valued variables are used to enumerate answers to certain combinatorial problems. ( This morning, the exposition http://www.cs.cornell.edu/courses/cs485/2006sp/lecture notes/lecture11.pdf is the first of many hits on the subject.)
Is there a useful generalization of the idea of generating functions that would employ operations on other structures? - matrices, for example.
Is there a useful generalization of the idea of generating functions that would employ operations on other structures? - matrices, for example.